The Hebrew word translated "make atonement" is chafar and means "to cover," specifically to cover over sin. (See, for example, Gesenius' Hebrew lexicon). Thus, this censing of the people constituted an atonement, specifically for their sin on that occasion of grumbling against Moses and Aaron because God had executed the rebellious Korah and his associates for trying to usurp the priesthood. It is a simple matter that any means God ordains for bringing about atonement will be effectual!
Theologically, however, this may cause problems for us Christians because we are used to the atonement provided by Jesus through his blood. In the NT the writer to the Hebrews states: "And almost all things are by the law purged with blood; and without the shedding of blood is no remission." (Heb. 9:22) That was the usual requirement of the Law, but the guilt incurred in the grumbling over Korah's rebellion and its remedy did not involve a standard requirement of law, but was dealt with according to God's specific instructions on that occasion.
According to Hebrews even the provisions of the old Law were only satisfactory up to a point. "For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: how much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God." (Heb. 9:13-14) We might say, then, that those provisions made for typical justification, but not the final atonement provided through Christ. That would also be true of Aaron's censing the people on the occasion under consideration.
Then how could it be said that the censing was atoning at all? In that it was done by the high priest. It was not any Israelite simply praying for the people, it was the high priest. And who is our High Priest? Jesus Christ! When he intercedes for us before the throne of God, he is asking that the benefits of his atonement be applied on our behalf. (Rom. 8:34) That is the antitypical incense.
So to answer your question, Yes, when Aaron censed the people on that particular occasion, he was making atonement and foreshadowing the good things to come.
By the way, the Hebrew word for "atone" which I could not incorporate into my text is כקר